Credit risk with Python R

Dr. Martín Lozano.

Abstract

This material

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library(ggplot2)

1 Credit VaR example 24.7.

This replicates Hull (2015) example 24.7.

This is the Vasicek model (equation 24.10) in a function form.

CVaR <- function(exp, pd, r, c, l) {
v <- pnorm((qnorm(pd) + (c^0.5) * qnorm(l)) / (1 - c)^0.5)
VaR <- exp * v * (1 - r)
}

See if it works. Let’s evaluate equation 24.10 at 99% and 99.9%. The 1-year 99% and 99.9% credit VaR is:

CVaR.999 <- CVaR(100, 0.02, 0.6, 0.1, 0.999)
CVaR.99 <- CVaR(100, 0.02, 0.6, 0.1, 0.99)
CVaR.999

## [1] 5.129484

CVaR.99

## [1] 3.294271

Let’s evaluate the model at all confidence levels (from 0 to 1) simulating 10,000 values.

set.seed(13)
l <- runif(10000, 0, 1)
Loss <- CVaR(100, 0.02, 0.6, 0.1, l)
sim.var999 <- sort(Loss)[10000 * 0.999]
sim.var99 <- sort(Loss)[10000 * 0.99]

Now, visually:

hist(Loss, 100, xlim = c(0, 7), xlab = "Losses in millions", main = NULL)
abline(v = CVaR.999, lty = 2, col = "red", lwd = 2)
abline(v = CVaR.99, lty = 2, col = "blue", lwd = 2)
legend("topright", legend = c("1-year 99% credit VaR is 3.294271", 
         "1-year 99.9% credit VaR is 5.129484"),
col = c("blue", "red"), lwd = 2, lty = 2, bg = "white", cex = 0.8)

Figure 1.1: Distribution of losses.

dat <- data.frame(Loss, l)
ggplot(dat, aes(x = Loss, fill = "Losses in millions")) + 
  geom_density(color = "darkblue", fill = "lightblue") +
  geom_vline(aes(xintercept = CVaR.999), 
             color = "red", linetype = "dashed", size = 1) +
  geom_vline(aes(xintercept = CVaR.99 ),   
             color = "blue", linetype = "dashed", size = 1) +
  scale_x_continuous(labels = scales::dollar)

Figure 1.2: Distribution of losses with ggplot.

Nice.

vector = list(range(11))
print(vector)

## [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

import numpy as np

vector = np.arange(11)
print(vector)

## [ 0  1  2  3  4  5  6  7  8  9 10]

import numpy as np
vector = np.arange(11)
print(vector)

## [ 0  1  2  3  4  5  6  7  8  9 10]

import pandas as pd

# Read the CSV file into a DataFrame
df = pd.read_csv('cr_loan2.csv')

# Access and process the data as needed
print(df.head())  # Print the first few rows of the DataFrame

##    person_age  ...  cb_person_cred_hist_length
## 0          22  ...                           3
## 1          21  ...                           2
## 2          25  ...                           3
## 3          23  ...                           2
## 4          24  ...                           4
## 
## [5 rows x 12 columns]

# Check the structure of the data
print(df.dtypes)

## person_age                      int64
## person_income                   int64
## person_home_ownership          object
## person_emp_length             float64
## loan_intent                    object
## loan_grade                     object
## loan_amnt                       int64
## loan_int_rate                 float64
## loan_status                     int64
## loan_percent_income           float64
## cb_person_default_on_file      object
## cb_person_cred_hist_length      int64
## dtype: object

# Check the first five rows of the data
pd.set_option('display.max_columns', None)
print(df.head())

##    person_age  person_income person_home_ownership  person_emp_length   
## 0          22          59000                  RENT              123.0  \
## 1          21           9600                   OWN                5.0   
## 2          25           9600              MORTGAGE                1.0   
## 3          23          65500                  RENT                4.0   
## 4          24          54400                  RENT                8.0   
## 
##   loan_intent loan_grade  loan_amnt  loan_int_rate  loan_status   
## 0    PERSONAL          D      35000          16.02            1  \
## 1   EDUCATION          B       1000          11.14            0   
## 2     MEDICAL          C       5500          12.87            1   
## 3     MEDICAL          C      35000          15.23            1   
## 4     MEDICAL          C      35000          14.27            1   
## 
##    loan_percent_income cb_person_default_on_file  cb_person_cred_hist_length  
## 0                 0.59                         Y                           3  
## 1                 0.10                         N                           2  
## 2                 0.57                         N                           3  
## 3                 0.53                         N                           2  
## 4                 0.55                         Y                           4

This document took 0.08 minutes to compile in Rmarkdown, R version 4.2.1 (2022-06-23 ucrt).

References.

Hull, John C. 2015. Options, Futures, and Other Derivatives. 9th ed. Prentice Hall.